yes if one of the wires was getting an earth from the alternator cover or rubbing off the engine the battery light is really an alternator light warning you that the alternator is not charging the battery
I would have the alternator tested. If the alternator is over charging the battery then it is just cooking it.
either the alternator is dischargeing the battery or it is going flat just because its not getting re charged
Battery light usually means alternator not charging. Most common solutions would be be a bad alternator, bad connection, or loose alternator belt. If the battery and alt test ok than check the connections to the alternator and battery. The alternator should have 2 connections.
Spark plugs don't smoke. A bad alternator would cause a dead battery.
A short in the wiring.
Battery light usually means alternator not charging. Most common solutions would be be a bad alternator, bad connection, or loose alternator belt. If the battery and alt test ok than check the connections to the alternator and battery.
the alternator is out
Shorted diodes in the alternator.
Overcharging by the alternator or if it is connected in reverse polarity.
A bad alternator will cause a battery to go bad. It does not have an effect on the air conditioner.
Yes, since it would not return power to the battery.
It would if the battery voltage was lowered enough to cause it not to fire.